Metamath Proof Explorer


Theorem e200

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e200.1
|- (. ph ,. ps ->. ch ).
e200.2
|- th
e200.3
|- ta
e200.4
|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion e200
|- (. ph ,. ps ->. et ).

Proof

Step Hyp Ref Expression
1 e200.1
 |-  (. ph ,. ps ->. ch ).
2 e200.2
 |-  th
3 e200.3
 |-  ta
4 e200.4
 |-  ( ch -> ( th -> ( ta -> et ) ) )
5 2 vd02
 |-  (. ph ,. ps ->. th ).
6 3 vd02
 |-  (. ph ,. ps ->. ta ).
7 1 5 6 4 e222
 |-  (. ph ,. ps ->. et ).